Exercise , Chapter 12

setwd("/Users/Nashrah/Desktop/Columbia_QMSS/Spring 2018 Courses/Advanced Regression Modeling")
df <- read.delim2("NES.txt", header = TRUE, sep = " ", dec = ".")
write.table(df, file="NES.dat", row.names=TRUE)
NES <- read.table("NES.dat", header = TRUE)

NES_sub <- NES$year==1992 & !is.na(NES$rvote) & !is.na(NES$dvote) & (NES$rvote==1 | NES$dvote==1)
NES92 <- NES[NES_sub,]

# logistic regression of vote preference on income

fit_1 <- glm(rvote ~ income, family=binomial(link="logit"), data=NES92)
display(fit_1)
## glm(formula = rvote ~ income, family = binomial(link = "logit"), 
##     data = NES92)
##             coef.est coef.se
## (Intercept) -1.40     0.19  
## income       0.33     0.06  
## ---
##   n = 1179, k = 2
##   residual deviance = 1556.9, null deviance = 1591.2 (difference = 34.3)
stan_fit_1 <- stan_glm(rvote ~ income, family=binomial(link="logit"), data=NES92)
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print(stan_fit_1)
## stan_glm
##  family:       binomial [logit]
##  formula:      rvote ~ income
##  observations: 1179
##  predictors:   2
## ------
##             Median MAD_SD
## (Intercept) -1.4    0.2  
## income       0.3    0.1  
## 
## Sample avg. posterior predictive distribution of y:
##          Median MAD_SD
## mean_PPD 0.4    0.0   
## 
## ------
## For info on the priors used see help('prior_summary.stanreg').
fit_2 <- glm(rvote ~ income + educ2 + str_partyid, family=binomial(link="logit"), data=NES92)
display(fit_2)
## glm(formula = rvote ~ income + educ2 + str_partyid, family = binomial(link = "logit"), 
##     data = NES92)
##             coef.est coef.se
## (Intercept) -1.52     0.30  
## income       0.28     0.06  
## educ2        0.07     0.04  
## str_partyid -0.02     0.06  
## ---
##   n = 1178, k = 4
##   residual deviance = 1552.8, null deviance = 1590.2 (difference = 37.4)
stan_fit_2 <- stan_glm(rvote ~ income + educ2 + str_partyid, family=binomial(link="logit"), data=NES92)
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print(stan_fit_2)
## stan_glm
##  family:       binomial [logit]
##  formula:      rvote ~ income + educ2 + str_partyid
##  observations: 1178
##  predictors:   4
## ------
##             Median MAD_SD
## (Intercept) -1.5    0.3  
## income       0.3    0.1  
## educ2        0.1    0.0  
## str_partyid  0.0    0.1  
## 
## Sample avg. posterior predictive distribution of y:
##          Median MAD_SD
## mean_PPD 0.4    0.0   
## 
## ------
## For info on the priors used see help('prior_summary.stanreg').
fit_3 <- glm(rvote ~ income + educ2 + black + female + str_partyid, family=binomial(link="logit"), data=NES92)
display(fit_3)
## glm(formula = rvote ~ income + educ2 + black + female + str_partyid, 
##     family = binomial(link = "logit"), data = NES92)
##             coef.est coef.se
## (Intercept) -1.26     0.32  
## income       0.23     0.07  
## educ2        0.06     0.04  
## black       -2.68     0.37  
## female      -0.08     0.13  
## str_partyid  0.04     0.07  
## ---
##   n = 1178, k = 6
##   residual deviance = 1446.2, null deviance = 1590.2 (difference = 144.0)
stan_fit_3 <- stan_glm(rvote ~ income + educ2 + black + female + str_partyid, family=binomial(link="logit"), data=NES92)
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print(stan_fit_3)
## stan_glm
##  family:       binomial [logit]
##  formula:      rvote ~ income + educ2 + black + female + str_partyid
##  observations: 1178
##  predictors:   6
## ------
##             Median MAD_SD
## (Intercept) -1.3    0.3  
## income       0.2    0.1  
## educ2        0.1    0.0  
## black       -2.7    0.4  
## female      -0.1    0.1  
## str_partyid  0.0    0.1  
## 
## Sample avg. posterior predictive distribution of y:
##          Median MAD_SD
## mean_PPD 0.4    0.0   
## 
## ------
## For info on the priors used see help('prior_summary.stanreg').
fit_4 <- glm(rvote ~ income + educ2 + black + female + ideo + str_partyid, family=binomial(link="logit"), data=NES92)
display(fit_4)
## glm(formula = rvote ~ income + educ2 + black + female + ideo + 
##     str_partyid, family = binomial(link = "logit"), data = NES92)
##             coef.est coef.se
## (Intercept) -4.08     0.44  
## income       0.10     0.08  
## educ2        0.24     0.05  
## black       -2.69     0.39  
## female       0.15     0.15  
## ideo         0.71     0.05  
## str_partyid -0.01     0.08  
## ---
##   n = 1133, k = 7
##   residual deviance = 1082.1, null deviance = 1534.1 (difference = 452.0)
stan_fit_4 <- stan_glm(rvote ~ income + educ2 + black + female + ideo + str_partyid, family=binomial(link="logit"), data=NES92)
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print(stan_fit_4)
## stan_glm
##  family:       binomial [logit]
##  formula:      rvote ~ income + educ2 + black + female + ideo + str_partyid
##  observations: 1133
##  predictors:   7
## ------
##             Median MAD_SD
## (Intercept) -4.1    0.5  
## income       0.1    0.1  
## educ2        0.2    0.1  
## black       -2.7    0.4  
## female       0.2    0.2  
## ideo         0.7    0.0  
## str_partyid  0.0    0.1  
## 
## Sample avg. posterior predictive distribution of y:
##          Median MAD_SD
## mean_PPD 0.4    0.0   
## 
## ------
## For info on the priors used see help('prior_summary.stanreg').
#selected model:
fit_4 <- glm(rvote ~ income + educ2 + income:educ2 + black + female, family=binomial(link="logit"), data=NES92)
display(fit_4)
## glm(formula = rvote ~ income + educ2 + income:educ2 + black + 
##     female, family = binomial(link = "logit"), data = NES92)
##              coef.est coef.se
## (Intercept)  -1.15     0.49  
## income        0.24     0.17  
## educ2         0.07     0.12  
## black        -2.67     0.37  
## female       -0.09     0.13  
## income:educ2  0.00     0.04  
## ---
##   n = 1179, k = 6
##   residual deviance = 1447.9, null deviance = 1591.2 (difference = 143.3)
stan_fit_4 <- stan_glm(rvote ~ income + educ2 + income:educ2 + black + female, family=binomial(link="logit"), data=NES92)
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print(stan_fit_4)
## stan_glm
##  family:       binomial [logit]
##  formula:      rvote ~ income + educ2 + income:educ2 + black + female
##  observations: 1179
##  predictors:   6
## ------
##              Median MAD_SD
## (Intercept)  -1.2    0.5  
## income        0.2    0.2  
## educ2         0.1    0.1  
## black        -2.7    0.4  
## female       -0.1    0.1  
## income:educ2  0.0    0.0  
## 
## Sample avg. posterior predictive distribution of y:
##          Median MAD_SD
## mean_PPD 0.4    0.0   
## 
## ------
## For info on the priors used see help('prior_summary.stanreg').
#the textbook recommends using the following tricks to best interpret the results:
#1)evaluate predictions from the mean of variables and to divide by 4 to get approximate predictive differences on the prob scale
#intercept: logit^-1(-1.15+.24*3.1+0.07*4.3-2.67*0.133-0.09*0.533+0*3.1*4.3) = ~ -0.5
#income: 3.1
#education: 4.3
#black: 0.133
#female: 0.553

#having a little bit of a hard time understanding how to implement these steps for the above regression 

Exercise 2, Chapter 12

test.

test.